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Numerical Solution of the Discrete BHH-Equation in the Normal Case

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Abstract

It is known that the solution of the semilinear matrix equation \(X - A\overline X B = C\) can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. We propose a method for solving the original semilinear equation in the normal case that permits to almost halve the execution time for equations of order n = 3000 compared to the library function dlyap, which solves Stein equations in Matlab.

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References

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Authors and Affiliations

  1. LomonosovMoscow State University, Leninskie Gory, GSP-1, Moscow, 119991, Russia

    Kh. D. Ikramov

  2. GlobusMedia Ltd., 1st Nagatinskii proezd 10, Moscow, 115230, Russia

    Yu. O. Vorontsov

Authors
  1. Kh. D. Ikramov
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  2. Yu. O. Vorontsov
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Correspondence to Kh. D. Ikramov.

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Original Russian Text © Kh.D. Ikramov, Yu.O. Vorontsov, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 4, pp. 367–373.

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Ikramov, K.D., Vorontsov, Y.O. Numerical Solution of the Discrete BHH-Equation in the Normal Case. Numer. Analys. Appl. 11, 293–297 (2018). https://doi.org/10.1134/S199542391804002X

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  • DOI: https://doi.org/10.1134/S199542391804002X

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